GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 09 Dec 2018, 20:22

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Algebra Webinar

     December 09, 2018

     December 09, 2018

     07:00 AM PST

     09:00 AM PST

    Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
  • Free lesson on number properties

     December 10, 2018

     December 10, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

Is (x+y)(x-y) = even integer?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1236
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post Updated on: 07 Apr 2015, 03:40
5
6
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

22% (01:29) correct 78% (01:24) wrong based on 192 sessions

HideShow timer Statistics

Is \((x+y)(x-y) =\) even integer?

1) \(x^2+y^2 =\) even

2) \(x+y =\)even

Source: self-made

_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)


Originally posted by Harley1980 on 06 Apr 2015, 10:19.
Last edited by Harley1980 on 07 Apr 2015, 03:40, edited 3 times in total.
Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8649
Location: Pune, India
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 07 Apr 2015, 01:08
5
2
Harley1980 wrote:
Is \((x+y)(x-y) =\) even integer?

1) \(x^2+y^2 =\) even

2) \(x+y =\)even


So now the question is - what is the actual answer?

Try using both statements together: If you know that \(x + y\) is an even integer and \(x^2 + y^2\) is an even integer, is it necessary that \(x^2 - y^2\) should be an even integer too? Actually, no!

It is easy to show that if x and y are both even/both odd integers, then \(x+y\) is even, \(x^2 + y^2\) is even and \(x^2 - y^2\) is even.

But how do you figure out a case where \(x+y\) is even, \(x^2 + y^2\) is even but \(x^2 - y^2\) is not an even integer?

Let me give you an example: Say \(x = 3+\sqrt{6}\) and \(y = 3 - \sqrt{6}\).

Here, \(x + y = 6\) (even integer)
\(x^2 + y^2 = 30\) (even integer)
But \(x^2 - y^2 = 12\sqrt{6}\)

So answer is (E).

What you should think about is: How can you prove with variables that answer is (E)? Perhaps, the form of x and y that I have given as an example can help you!
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

General Discussion
Manager
Manager
avatar
S
Joined: 13 Nov 2014
Posts: 109
GMAT 1: 740 Q50 V40
Reviews Badge
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 06 Apr 2015, 13:22
Am i missing something simple?

A)(x+y)(x-y) = x^2+y^2 and we are told that is even... so suff

B) we are told (x+y) is even. even * even = even and odd * even = even . Even if (x-y) = 0, gmat considers 0 as even. So Suff
_________________

Gmat prep 1 600
Veritas 1 650
Veritas 2 680
Gmat prep 2 690 (48Q 37V)
Gmat prep 5 730 (47Q 42V)
Gmat prep 6 720 (48Q 41V)

Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1236
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 06 Apr 2015, 13:30
Wofford09 wrote:
Am i missing something simple?

A)(x+y)(x-y) = x^2+y^2 and we are told that is even... so suff

B) we are told (x+y) is even. even * even = even and odd * even = even . Even if (x-y) = 0, gmat considers 0 as even. So Suff


about A) \((x+y)(x-y)\) not equal to \(x^2+y^2\) it is equal to \(x^2-y^2\)

about B)
Let's assume that \(x =\frac{5}{3}\) and \(y = \frac{1}{3}\), \(x + y = \frac{5}{3}+\frac{1}{3} = \frac{6}{3} = 2\)

but \(x^2+y^2\) will be equal to \((\frac{5}{3})^2 + (\frac{1}{3})^2 = \frac{25}{9}+\frac{1}{9} =\frac{26}{9}\) not even
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8649
Location: Pune, India
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 06 Apr 2015, 19:50
1
Harley1980 wrote:
Wofford09 wrote:
Am i missing something simple?

A)(x+y)(x-y) = x^2+y^2 and we are told that is even... so suff

B) we are told (x+y) is even. even * even = even and odd * even = even . Even if (x-y) = 0, gmat considers 0 as even. So Suff


about A) \((x+y)(x-y)\) not equal to \(x^2+y^2\) it is equal to \(x^2-y^2\)

about B)
Let's assume that \(x =\frac{5}{3}\) and \(y = \frac{1}{3}\), \(x + y = \frac{5}{3}+\frac{1}{3} = \frac{6}{3} = 2\)

but \(x^2+y^2\) will be equal to \((\frac{5}{3})^2 + (\frac{1}{3})^2 = \frac{25}{9}+\frac{1}{9} =\frac{26}{9}\) not even


Using the same logic, think what happens in stmnt 1 when \(x^2 = 5/3\) and \(y^2 = 1/3\).
In this case, \(x^2 + y^2 = 2\) (even) but \(x^2 - y^2 = 4/3\) (not an even integer)
but if \(x^2 = 12\) and \(y^2 = 6\), both \(x^2 + y^2\) and \(x^2 - y^2\) are even.
So how can the answer be (A)?
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1236
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 06 Apr 2015, 22:15
VeritasPrepKarishma wrote:
Harley1980 wrote:
Wofford09 wrote:
Am i missing something simple?

A)(x+y)(x-y) = x^2+y^2 and we are told that is even... so suff

B) we are told (x+y) is even. even * even = even and odd * even = even . Even if (x-y) = 0, gmat considers 0 as even. So Suff


about A) \((x+y)(x-y)\) not equal to \(x^2+y^2\) it is equal to \(x^2-y^2\)

about B)
Let's assume that \(x =\frac{5}{3}\) and \(y = \frac{1}{3}\), \(x + y = \frac{5}{3}+\frac{1}{3} = \frac{6}{3} = 2\)

but \(x^2+y^2\) will be equal to \((\frac{5}{3})^2 + (\frac{1}{3})^2 = \frac{25}{9}+\frac{1}{9} =\frac{26}{9}\) not even


Using the same logic, think what happens in stmnt 1 when \(x^2 = 5/3\) and \(y^2 = 1/3\).
In this case, \(x^2 + y^2 = 2\) (even) but \(x^2 - y^2 = 4/3\) (not an even integer)
but if \(x^2 = 12\) and \(y^2 = 6\), both \(x^2 + y^2\) and \(x^2 - y^2\) are even.
So how can the answer be (A)?



Wow, that's amazing. VeritasPrepKarishma, you have an eagle eye )
Thank you.
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Manager
Manager
avatar
Joined: 17 Mar 2015
Posts: 116
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post Updated on: 06 Apr 2015, 23:22
My solution:
For the first option: \(X^2 + Y^2 =\) even, then if you add or subtract \(2*X*Y\), you will get an even number aswell, so \(X^2 + Y^2 + 2*X*Y = (X + Y)^2\) is even and \((X - Y)^2\) is even too. Say both of them are \(2*k\) and \(2*b\) respectively.
\(\sqrt{2*k}*\sqrt{2*b} = 2*\sqrt{k}*\sqrt{b}\) which is even, thus #1 is sufficient.
For the second - well, its quite obvious: product of even number with whatever = even, thats true, thus sufficient

C it is then
edit: meant D, which is, sadly, incorrect.

Originally posted by Zhenek on 06 Apr 2015, 23:11.
Last edited by Zhenek on 06 Apr 2015, 23:22, edited 1 time in total.
Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1236
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 06 Apr 2015, 23:15
Zhenek wrote:
My solution:
For the first option: \(X^2 + Y^2 =\) even, then if you add or subtract \(2*X*Y\), you will get an even number aswell, so \(X^2 + Y^2 + 2*X*Y = (X + Y)^2\) is even and \((X - Y)^2\) is even too. Say both of them are \(2*k\) and \(2*b\) respectively.
\(\sqrt{2*k}*\sqrt{2*b} = 2*\sqrt{k}*\sqrt{b}\) which is even, thus #1 is sufficient.
For the second - well, its quite obvious: product of even number with whatever = even, thats true, thus sufficient

C it is then


Zhenek, this is look as you say that answer D is right: both statements are sufficient by themselves. Am I right?
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Manager
Manager
avatar
Joined: 17 Mar 2015
Posts: 116
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post Updated on: 07 Apr 2015, 01:35
Harley1980 wrote:
Zhenek wrote:
My solution:
For the first option: \(X^2 + Y^2 =\) even, then if you add or subtract \(2*X*Y\), you will get an even number aswell, so \(X^2 + Y^2 + 2*X*Y = (X + Y)^2\) is even and \((X - Y)^2\) is even too. Say both of them are \(2*k\) and \(2*b\) respectively.
\(\sqrt{2*k}*\sqrt{2*b} = 2*\sqrt{k}*\sqrt{b}\) which is even, thus #1 is sufficient.
For the second - well, its quite obvious: product of even number with whatever = even, thats true, thus sufficient

C it is then


Zhenek, this is look as you say that answer D is right: both statements are sufficient by themselves. Am I right?

Oh, yea, I guess I meant that indeed, not experienced with the gmat thing yet. Looks like my answer is wrong then, what a bummer. I guess I really need to pay attention to the given info (no information given about X and Y being non-integers, which completely blows my solution from the get-go: \(2*X*Y\) could be \(2*\sqrt{5}/2*\sqrt{3}/2\) which is not even remotely even )

Originally posted by Zhenek on 06 Apr 2015, 23:18.
Last edited by Zhenek on 07 Apr 2015, 01:35, edited 2 times in total.
Manager
Manager
avatar
Joined: 17 Mar 2015
Posts: 116
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 07 Apr 2015, 01:38
1
1
Well then, lets amend my approach. Lets start from get-go.

Looking at 1st option and taking into account the fact that X and Y could be non-integers, we can't really say anything about the answer to the question with just option 1 on its own, I'd just call it insufficient right away after comming up with 2 different examples, one being integer and another - non-integer.
Easiest ones that come into mind are:
1)X = 1, Y = 1: 2 is even, 0 is even
2)X = \(\sqrt{5}/2\), Y = \(\sqrt{3}/2\): 2 is even, 1/2 is not even
This makes #1 insufficient on its own.

#2 - same story, take fractions as second example and integers as first example, insufficient on its own.

Now lets look at them together
\(x^2 + y^2 = 2*k\)
\(x + y = 2*m\) => \(y = 2*m - x\)
\(x^2 + y^2 = (x+y)^2 - 2*x*y = (x+y)^2 - 2*x*(2*m-x) = 4*m^2 -2*x*(2*m - x) = 2*k\)
\(2*k = 4*m^2 - 2*x*(2*m - x)\) => \(x^2 -2*m*x + 2*m^2 - k = 0\)
\(x = m\)±\(\sqrt{k - m^2}\)
\(y = 2*m - x = m\)∓\(\sqrt{k - m^2}\)
So we found values of X and Y that would match 2 of these equation(both #1 and #2). That being said, k and m are random positive integers thus we can't be sure if the expression under the root is a perfect square or not.
If you input these values into your question, you will get \(x^2 - y^2 = (x-y)*(x+y) =\)±\(4*m*\sqrt{k - m^2}\) which unfortunatelly doesn't answer our question coz of root's value being uncertain (perfect square, then answer is "even", if it is not perfect square, then answer is "not even")
The answer E, yet again, contradicts the OA, which is unfortunate.
Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1236
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 07 Apr 2015, 03:43
Looks like my first attempt to make a task became a train wreck :(

VeritasPrepKarishma, Zhenek thanks for your explanations, it is now clear. I've changed answer to E.
Looks like this isn't 600-700 lvl task.
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Manager
Manager
avatar
S
Joined: 21 Oct 2017
Posts: 81
Location: France
Concentration: Entrepreneurship, Technology
GMAT 1: 750 Q48 V44
GPA: 4
WE: Project Management (Internet and New Media)
Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 28 Nov 2017, 11:04
I had a hard time with this question.

I would like to better understand what went wrong in my approach:

The question is: \((X + Y)(X - Y)\) = Even?
Which I rephrased too: \(X^2 + Y^2 - 2XY\) = Even?
Hence, when looking at statement 1 and 2, I'm able to asses that X and Y need to either both be Even or Odd, and \(2XY\) has to be Even. So I just went on to select D. :(

Please help me understand why I can't take this shortcut and I fell right into it.

Thanks,
_________________

Please Press +1 Kudos if it helps!

October 9th, 2017: Diagnostic Exam - Admit Master (GoGMAT) - 640
November 11th, 2017: CAT 1 - Admit Master (GoGMAT) - 700
November 20th, 2017: CAT 2 - GMATPrep - 700 (Q: 47, V: 40)
November 25th, 2017: CAT 3 - Admit Master (GoGMAT) - 710 (Q: 48, V: 40)
November 27th, 2017: CAT 4 - GMATPrep - 720 (Q: 49, V: 40)

December 4th, 2017: GMAT Exam - 750 (Q: 48, V: 44, IR: 8, AWA: 6)

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8649
Location: Pune, India
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 29 Nov 2017, 02:38
Hadrienlbb wrote:
I had a hard time with this question.

I would like to better understand what went wrong in my approach:

The question is: \((X + Y)(X - Y)\) = Even?
Which I rephrased too: \(X^2 + Y^2 - 2XY\) = Even?
Hence, when looking at statement 1 and 2, I'm able to asses that X and Y need to either both be Even or Odd, and \(2XY\) has to be Even. So I just went on to select D. :(

Please help me understand why I can't take this shortcut and I fell right into it.

Thanks,


Note that \((X + Y)*(X - Y) = X^2 - Y^2\)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
Manager
avatar
S
Joined: 21 Oct 2017
Posts: 81
Location: France
Concentration: Entrepreneurship, Technology
GMAT 1: 750 Q48 V44
GPA: 4
WE: Project Management (Internet and New Media)
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 30 Nov 2017, 17:06
OMG :shocked :shocked

I swear I have not been drinking. Just working too hard! Nonetheless, this is unacceptable of me. Thanks very much Karishma, and forgive my carelessness.

VeritasPrepKarishma wrote:
Hadrienlbb wrote:
I had a hard time with this question.

I would like to better understand what went wrong in my approach:

The question is: \((X + Y)(X - Y)\) = Even?
Which I rephrased too: \(X^2 + Y^2 - 2XY\) = Even?
Hence, when looking at statement 1 and 2, I'm able to asses that X and Y need to either both be Even or Odd, and \(2XY\) has to be Even. So I just went on to select D. :(

Please help me understand why I can't take this shortcut and I fell right into it.

Thanks,


Note that \((X + Y)*(X - Y) = X^2 - Y^2\)

_________________

Please Press +1 Kudos if it helps!

October 9th, 2017: Diagnostic Exam - Admit Master (GoGMAT) - 640
November 11th, 2017: CAT 1 - Admit Master (GoGMAT) - 700
November 20th, 2017: CAT 2 - GMATPrep - 700 (Q: 47, V: 40)
November 25th, 2017: CAT 3 - Admit Master (GoGMAT) - 710 (Q: 48, V: 40)
November 27th, 2017: CAT 4 - GMATPrep - 720 (Q: 49, V: 40)

December 4th, 2017: GMAT Exam - 750 (Q: 48, V: 44, IR: 8, AWA: 6)

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8649
Location: Pune, India
Re: Is (x+y)(x-y) = even integer?  [#permalink]

Show Tags

New post 30 Nov 2017, 23:30
Hadrienlbb wrote:
OMG :shocked :shocked

I swear I have not been drinking. Just working too hard! Nonetheless, this is unacceptable of me. Thanks very much Karishma, and forgive my carelessness.

VeritasPrepKarishma wrote:
Hadrienlbb wrote:
I had a hard time with this question.

I would like to better understand what went wrong in my approach:

The question is: \((X + Y)(X - Y)\) = Even?
Which I rephrased too: \(X^2 + Y^2 - 2XY\) = Even?
Hence, when looking at statement 1 and 2, I'm able to asses that X and Y need to either both be Even or Odd, and \(2XY\) has to be Even. So I just went on to select D. :(

Please help me understand why I can't take this shortcut and I fell right into it.

Thanks,


Note that \((X + Y)*(X - Y) = X^2 - Y^2\)


:) It is better to make these errors during practice so that you do not make them during the actual exam!!
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

GMAT Club Bot
Re: Is (x+y)(x-y) = even integer? &nbs [#permalink] 30 Nov 2017, 23:30
Display posts from previous: Sort by

Is (x+y)(x-y) = even integer?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.